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Decidability of all minimal models

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Types for Proofs and Programs (TYPES 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1158))

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Abstract

We consider a simply typed λ-calculus with constants of ground types, and assume that for one ground type o, there are finitely many constants of type o. We call minimal model the quotient by observational equivalence of the set of all closed terms whose type is of terminal subformula o. We show that this model is decidable: all classes of any given type are recursively representable, and observational equivalence on closed terms is a decidable relation. In particular, this result solves the question raised by R.Statman on the decidability of this model in the case of a unique ground type and two constants.

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Authors and Affiliations

  1. Equipe de Logique Mathématique, Université PARIS VII-C.N.R.S U.R.A. 753, 2 Place Jussieu - Case 7012, 75251, Paris Cedex 05, France

    Vincent Padovani

Authors
  1. Vincent Padovani
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Stefano Berardi Mario Coppo

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© 1996 Springer-Verlag Berlin Heidelberg

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Padovani, V. (1996). Decidability of all minimal models. In: Berardi, S., Coppo, M. (eds) Types for Proofs and Programs. TYPES 1995. Lecture Notes in Computer Science, vol 1158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61780-9_71

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  • DOI: https://doi.org/10.1007/3-540-61780-9_71

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61780-8

  • Online ISBN: 978-3-540-70722-6

  • eBook Packages: Springer Book Archive

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